The critical points of linear combinations of harmonic functions

On the Linear Combinations of Slanted Half-Plane Harmonic Mappings

‎In this paper,  the sufficient conditions for the linear combinations of slanted half-plane harmonic mappings to be univalent and convex in the direction of $(-gamma) $ are studied. Our result improves some recent works. Furthermore, a illustrative example and imagine domains of the linear combinations satisfying the desired conditions are enumerated.

On the Critical Points of Harmonic Functions

the effect of using critical discourse analytical tools on the improvement of the learners level of critical thinking in reading comprehension

?it is of utmost priority for an experienced teacher to train the mind of the students, and enable them to think critically and correctly. the most important question here is that how to develop such a crucial ability? this study examines a new way to the development of critical thinking utilizing critical discourse analytical tools. to attain this goal, two classes of senior english la...

Critical Points of Harmonic Functions on Domains In/?3

It is shown that the critical point relations of Morse theory, together with the maximum principle, comprise a complete set of critical point relations for harmonic functions of three variables. The proof proceeds by first constructing a simplified example and then developing techniques to modify this example to realize all admissible possibilities. Techniques used differ substantially from tho...

on the effect of linear & non-linear texts on students comprehension and recalling

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